Solve 1.5^t=16

$$1.5 ^ { t } = 16$$

Solve for t

$$t=4\log_{1.5}\left(2\right)\approx 6.838045165$$

Steps Using Definition of Logarithm

Use the rules of exponents and logarithms to solve the equation.

$$1.5^{t}=16$$

Take the logarithm of both sides of the equation.

$$\log(1.5^{t})=\log(16)$$

The logarithm of a number raised to a power is the power times the logarithm of the number.

$$t\log(1.5)=\log(16)$$

Divide both sides by \log(1.5).

$$t=\frac{\log(16)}{\log(1.5)}$$

By the change-of-base formula \frac{\log(a)}{\log(b)}=\log_{b}\left(a\right).

$$t=\log_{1.5}\left(16\right)$$